Arithmetic properties of q-Barnes polynomials
Résumé
By making use of some explicit relationships between the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Frobenius-Euler polynomials of higher order and the generalized Hurwitz-Lerch zeta function as well as a new expansion formula for the generalized Hurwitz-Lerch zeta function obtained recently by Gaboury and Bayad , in this paper we present some series representations for these polynomials at rational arguments. These results provide extensions of those obtained by Apostol (1951) and by Srivastava (2000).
Domaines
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A comme version hal-04464163 Article Abdelmejid Bayad. Arithmetic properties of q-Barnes polynomials. Journal of Computational Analysis and Applications, 2013, 15 (1), pp.111-117. ⟨hal-04464163⟩